with \(J_i^\mu \)  denoting the comoving current of the \(i\) th SM chiral fermion species.
The prefactors \(\varepsilon _i\) , \(g_i\) , and \(Y_i\)  are explained and listed in Tab. REF .
The ellipsis represents all other SM Yukawa and sphaleron processes that can impact the evolution of the fermion currents.
During inflation, these processes are inefficient, which allows us to neglect them in the computation of the fermion charges generated by the hypercharge gauge field.\(5\endcsname \)A possible exception to this is the top-quark Yukawa coupling, which may not be fully negligible during inflation.
If efficient, this interaction could (i) reshuffle the fermionic chemical potentials, (ii) modify the top-quark contribution to the induced current, and (iii) contribute to the Higgs potential [1]}.
For the purposes of this work, the first point is irrelevant, as the interactions in the thermal plasma after inflation will in any case lead to a \(CP\) -conserving reshuffling of the chemical potentials.
The second point will induce at the very most an error of about \(16\,\%\) ; an estimate that we obtain if we completely drop all contributions of the third quark generation from the induced current.
For simplicity, we will also discard the third point, if necessary assuming an additional Hubble-induced contribution to the Higgs potential that stabilizes the vacuum expectation value of the Higgs field at the origin.

